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Über dieses Buch

This series of reference books describes sciences of different elds in and around geodesy with independent chapters. Each chapter covers an individual eld and describes the history, theory, objective, technology, development, highlights of research and applications. In addition, problems as well as future directions are discussed. The subjects of this reference book include Absolute and Relative Gravimetry, Adaptively Robust Kalman Filters with Applications in Navigation, Airborne Gravity Field Determination, Analytic Orbit Theory, Deformation and Tectonics, Earth Rotation, Equivalence of GPS Algorithms and its Inference, Marine Geodesy, Satellite Laser Ranging, Superconducting Gravimetry and Synthetic Aperture Radar Interferometry. These are individual subjects in and around geodesy and are for the rst time combined in a unique book which may be used for teaching or for learning basic principles of many subjects related to geodesy. The material is suitable to provide a general overview of geodetic sciences for high-level geodetic researchers, educators as well as engineers and students. Some of the chapters are written to ll literature blanks of the related areas. Most chapters are written by well-known scientists throughout the world in the related areas. The chapters are ordered by their titles. Summaries of the individual chapters and introductions of their authors and co-authors are as follows. Chapter 1 “Absolute and Relative Gravimetry” provides an overview of the gravimetric methods to determine most accurately the gravity acceleration at given locations.



Chapter 1. Absolute and Relative Gravimetry

Absolute and relative gravimetry allow the determination of gravity acceleration, usually just called gravity, for specific positions as well as the detection of gravity changes with time at a given location. For high-accuracy demands, the geometrical position of a gravity point has to be defined very accurately, e.g. in geodynamic research projects, at a height along the vertical above a ground mark. Geodetic networks with local, regional or global extent can be surveyed to monitor short-term and long-term gravity variations.

Ludger Timmen

Chapter 2. Adaptively Robust Kalman Filters with Applications in Navigation

A new adaptively robust Kalman filtering was developed in 2001. The main achievements of the adaptively robust filter are summarized from the published papers in recent years. These include the establishment of the principle of the adaptively robust filter, the derivation of the corresponding state parameter estimator, the developments of four adaptive factors for balancing the contribution of kinematic model information and measurements, which include three-segment function, two-segment function, exponential function and zero and one function for state component adaptation, and the establishment of four kinds of learning statistics for judging the kinematic model errors, which include state discrepancy statistic, predicted residual statistic, variance component ratio statistic and velocity discrepancy statistic. The relations of the adaptively robust filter with standard Kalman filter, robust filter and some other adaptive Kalman filters as well as some related adjustment methods are depicted by a figure. Other developments of the adaptively robust filter are also presented.

Yuanxi Yang

Chapter 3. Airborne Gravity Field Determination

Airborne measurement of gravity has long been a goal for geodesy and geophysics, both to serve geodetic needs (such as geoid determination) and in order to provide efficient and economic mapping of gravity anomalies for geophysical exploration. Although airborne gravimetry has been attempted since the 1960s (LaCoste 1967), it is only in the 1990s, with the development of carrier-phase kinematic GPS methods, that the accuracy has reached a useful level. In later years new gravity acceleration sensors and improved GPS processing methods have resulted in airborne survey accuracies of 1 mGal (10




) or less at a resolution of a few kilometers for several commercial operators (Williams and MacQueen 2001), typically operating in relatively small regions for geophysical exploration and flying during optimal conditions (e.g., at night when turbulence is minimal).

Rene Forsberg, Arne V. Olesen

Chapter 4. Analytic Orbit Theory

The desire to understand the orbits of the planets has a history as long as that of mankind. How and why the planets orbit around the Sun are questions in two categories. One focuses on geometry and the other on physics. Johannes Kepler (1571–1630) answered first the how with his laws of planetary motion in Astronomia nova (1609). Isaac Newton (1643–1727) answered both the how and why with his universal gravitation and laws of motion in

Principia Mathematica


Guochang Xu

Chapter 5. Deformation and Tectonics: Contribution of GPS Measurements to Plate Tectonics – Overview and Recent Developments

The use of space-geodetic techniques to study geodynamic processes began with Very Long Baseline Interferometry (VLBI) in the early 1970s. By measuring the delay in arrival time of the signal from distant celestial objects, the distances between stations that are hundreds of kilometres apart can be derived with millimetre accuracy. A review of the first 20 years of this technique is given by Ryan and Ma (1998). Around the world there are nowadays more than 100 VLBI stations. Another technique that has been available since the early 1970s is Satellite Laser Ranging (SLR). As the name implies, this technique determines the distance to a satellite by measuring the round trip time of a light pulse that is sent to the satellite (Degnan 1993). Today, there are about 60 SLR stations operational around the world.

Luisa Bastos, Machiel Bos, Rui Manuel Fernandes

Chapter 6. Earth Rotation

The rotation of the Earth varies continuously. Its rotation axis changes its orientation with respect to both a space-fixed and an Earth-fixed reference system, and the angular velocity of the rotation fluctuates with time. The knowledge and therewith the continuous observation of Earth rotation variations is important for various reasons. It is fundamental for the realisation of time systems, the accurate determination of reference frames and precise navigation by providing the link between an Earth-fixed and a space-fixed coordinate system. Moreover, time series of Earth rotation parameters are of great interest for various disciplines of geosciences and astronomy since their changes are related to gravitational and geodynamic processes in the Earth system. In this way, Earth rotation monitoring contributes significantly to the understanding of the dynamics of the Earth system and the interactions between its individual components, e.g. the exchange of angular momentum between atmosphere, ocean and solid Earth, or the coupling mechanism between the Earth’s core and mantle. Today the metrological basis for this highly interdisciplinary research is provided by precise space geodetic techniques such as Very Long Baseline Interferometry (VLBI), Satellite/Lunar Laser Ranging (SLR/LLR), Global Navigation Satellite Systems (GNSS) and ring laser gyroscopes.

Florian Seitz, Harald Schuh

Chapter 7. Equivalence of GPS Algorithms and Its Inference

In the past decade of GPS research, advantages and disadvantages of the differential and un-differential GPS have been discussed in detail in many publications. First in 2002 it was algebraically pointed out that the un-differential and differential algorithms of GPS are equivalent (Xu 2002a). Various combined and uncombined methods of GPS algorithms were discussed in detail too to show the advantages of some combining ways. However, again the combined and uncombined algorithms were proved to be equivalent (Xu et al.2006a, 2007). The equivalence principle can now be easily explained and accepted, because the used GPS data and model are the same and the used adjustment principle is also the same. The information contents are the same; therefore the results one may obtain should also be equivalent.

Guochang Xu, Yunzhong Shen, Yuanxi Yang, Heping Sun, Qin Zhang, Jianfeng Guo, Ta-Kang Yeh

Chapter 8. Marine Geodesy

Taking a look at our planet, we can easily realize that more than 70% of the Earth’s surface is covered by oceans and coastal waters. These waters have been the driving force of the climatic changes during the history of the planet. It is also the place where life started to develop and still the largest biosphere.

Joerg Reinking

Chapter 9. Satellite Laser Ranging

Determining the range to a satellite in orbit around the earth utilising the technique of satellite laser ranging (SLR) was pioneered in the early 1960s. The first successful ranging experiment was reported in the 3 December 1964 issue of Flight International (Smith 1964). Dr. Henry H. Plotkin of Goddard Space Flight Centre led a NASA team to track the Beacon-B (also known as Explorer-22) satellite for ten successful sessions during the period 11 October to 13 November 1964. A team from General Electric Co. (Valley Forge, Pennsylvania) also participated from Phoenix, Arizona. Using a telescope mounted with a ruby laser, expected range accuracy was about 3 m. Current accuracy is at the level of 1–2 cm.

Ludwig Combrinck

Chapter 10. Superconducting Gravimetry

The objective of gravimetry (Torge 1989) is the determination of the gravity field of the Earth and the surface gravity effects as functions of position and time by measurements of the gravity intensity which is the magnitude of the gravity acceleration


on the Earth’s surface. The gravity


and its variation depend on the mass attraction (law of gravitation) according to the arrangement of the terrestrial and exterritorial masses (celestial bodies) and the Earth rotation (centrifugal acceleration). Mass distribution and rotation are subject to variations in time.

Jürgen Neumeyer

Chapter 11. Synthetic Aperture Radar Interferometry

In the past two decades INSAR technique (synthetic aperture radar interferometry) has been quickly developed and widely used for the study of topography (digital elevation model generation) and deformation (Earth surface monitoring). Synthetic aperture radar (SAR) is a coherent active microwave image instrument, which is used for mapping the scattering properties of the Earth’s surface in the respective wavelength domain. The intensity (grey value) of each pixel in an SAR image represents the physical and geological property and geometric parameters of the imaged scene. In the late 1970s the first space-borne SAR system in the world (NASA satellite SEASAT) was launched for Earth observation. This mission pioneered the application of the SAR technology to mapping the Earth’s surface, acquiring information about physical and geological properties such as topography, morphology, moisture, and finding underground water. The space-borne SAR systems operate in the microwave range and therefore work on all days and all meteorological conditions.

Ye Xia


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